Question

write the equation of the asymptote(s) for the function graphed below. enter \dne\ in the an does not exist. vertical asymptote: horizontal asymptote: question help: video post to forum submit question

Explanation:

Step1: Identify vertical asymptote

A vertical asymptote occurs where the function approaches infinity or negative infinity. Looking at the graph, the function approaches infinity as \(x\) approaches \(- 2\). So the vertical asymptote is \(x=-2\).

Step2: Identify horizontal asymptote

A horizontal asymptote is a value \(y = k\) that the function approaches as \(x\to\pm\infty\). As \(x\to\pm\infty\), the function approaches \(y = - 2\). So the horizontal asymptote is \(y=-2\).

Answer:

Vertical Asymptote: \(x = - 2\)
Horizontal Asymptote: \(y=-2\)